Method and apparatus for improved depth matching of borehole images or core images

ABSTRACT

A method for depth matching borehole images and/or core section images is disclosed wherein signals from sensors at different levels on a logging tool are converted into an averaged signal representing the average bed signal at the center of the borehole at each of the different levels. A depth matching technique is applied to the averaged signals from the sensors at different levels on the logging tool to determine the optimum depth offset necessary for matching two sets of signals from sensors at the different levels of the logging tool. In an alternative embodiment of the invention a Hough transform is utilized to process the well log images and generate three-dimensional images in Hough space. The three dimensional images are converted into two-dimensional extremum curves. Depth matching is performed on the two dimensional extremum curves to calculate an offset to match the two dimensional extremum curves. The calculated offset is then applied to the well log images to depth match them.

FIELD OF THE INVENTION

This invention relates to logging of boreholes. More specifically, theinvention relates to a method for improving correlation of core images,borehole images and well logging data derived from sensors located on awell logging tool as it passes through a borehole.

BACKGROUND OF THE INVENTION

In a typical prior art oil well logging scenario, a string of welllogging tools having multiple sensors for measuring characteristics ofthe earth formation along the wall of a borehole is lowered via a cableto the bottom of the borehole. Geophysical data is recorded by way ofthe sensors as the cable is wound in using a precision winch. The depthin the earth at which the sensors on the logging tools are positioned asdata is logged is determined by measuring the logging speed and cabledepth. Devices such as a depth wheel measurement instrument and an axialaccelerometer may be utilized.

Typically, measurements taken along the length of a borehole by loggingtools are intended to provide indications of oil-bearing or gas-bearingstrata in the earth. In the prior art, measurements of variouscharacteristics or parameters of earth formations are usually obtainedby combining measurements (data logs) taken by way of multiple sensorsduring a single pass through the borehole, or taken during differentpasses through the same borehole. When combining such measurements it isnecessary that they be accurately correlated in depth with one anotherto be useful.

One problem is that the movement downhole of a tool with its sensors isusually not uniform. The non-uniform motion may be caused by such thingas: (a) damped longitudinal oscillations of the logging tool on thecable, (b) sticking and slipping of the logging tool against the sidesof a borehole or the wall of casing in the borehole, and (c) irregularmotion of the sensors that are mounted on mechanical arms that haveindependent motion with respect to the logging tool itself. As a resultof non-uniform motion of the logging tool, data collected by aparticular sensor on the logging tool at any specific depth in theborehole may not show as being recorded at the specific depth but at adifferent depth. Similarly, data from different sensors of the same toolmay not show as having been recorded at the same depth for all thosesensors.

To overcome the depth measurement problem in the prior art, a welllogging tool for measuring depth in a borehole is disclosed in U.S. Pat.No. 5,019,978, issued May 28, 1991 to Allen Q. Howard, Jr. and David J.Rossi. The invention in that patent provides for estimation of adominant mechanical resonant frequency parameter and of a dampingconstant parameter. These two parameters are taken into considerationwhen correcting an approximate indication of depth of a well loggingtool to determine the actual, true depth of the well logging tool in aborehole.

Besides measuring depth in a borehole, well logging seeks to measureother physical characteristics along the sides of the borehole such asfractures, bed boundaries and bed dips. A major advance in boreholelogging has been the development by Schlumberger of the FormationMicroscanner (“FMS”), a borehole imaging system. The FMS processingtechnique is described in U.S. Pat. No. 4,468,623 issued Aug. 28, 1984to Stanley C. Gianzero, David E. Palaith, and David S. K. Chan; and inU.S. Pat. No. 4,567,759 issued Feb. 5, 1986 to Michael P. Ekstrom andDavid S. K. Chan. The FMS system uses a tool having wall-engaging padseach carrying an array of electrical sensors distributed in thecircumferential direction with respect to the axis of the borehole.Signal voltages generated by the sensors are sampled as the well loggingtool moves along the borehole. The signals are processed and renderedvisible, by photographic or other printout, or by cathode-ray tubedisplay as a two-dimensional visible image is formed over loggedsegments of the borehole walls. In such images, bed boundaries can bevisually identified from sharp visible contrasts in the images, whichreflect sharp changes in resistivity at boundaries of the beds. Theimages thus obtained may exhibit a resolution on the order of 0.5 cm,allowing very fine details of the formation to be distinguished due tothe number of sensors in the circumferential direction, and the highrate of sampling in the longitudinal direction.

U.S. Pat. No. 4,251,773, issued Feb. 17, 1981 to Michel Cailliau andPhilippe Vincent teaches the use of signals from sensors to determinedip (inclination) and azimuth (strike) of bed boundaries. Morespecifically, this patent teaches a logging tool that has foursubstantially identical pads with sensors angularly distributed aboutthe axis of the logging tool in a side-by-side relationship and adaptedto engage the borehole wall at ninety-degree intervals. The sensorsprovide resistivity measurements of the respective sectors of theborehole wall engaged by the pads. As the logging tool is moved alongthe borehole wall, the sensors continuously provide signals measuringthe resistivity of the adjacent earth formation. Sharp variations inresistivity indicate boundaries between different beds in the earthformation. The signals produced by the sensors at different angularpositions of the pads are processed to provide information about the dipof bed boundaries, i.e., the orientations of the bed boundaries withrespect to a terrestrial reference, and the azimuth of the dip.

Another tool that is lowered into or withdrawn from a borehole and hasmultiple sensors that measure properties such as resistivity alongsegments of a borehole wall is taught in U.S. Pat. No. 5,960,371 issuedSep. 28, 1999 to Naoki Saito, Nicholas N. Bennett and Robert Burridge.This patent teaches use of the Hough transform to extract dip andazimuth of multiple fractures and beddings from any type of boreholeimage with respect to a terrestrial reference. The method is also robustenough to account for noise or gaps in the images. The method canseparate dips and azimuths of fractures from those of formations. Thus,it can detect and characterize other geometric features (e.g., linear,circular, or ellipsoidal shapes, some of which may represent vugs incarbonate reservoirs) present in the images.

As previously pointed out, when combining data of well logs it isnecessary that they be correlated in depth in order to be useful. Onemethod for depth correlation of well log data is taught in U.S. Pat. No.4,327,412 issued Apr. 27, 1982 to John P. Timmons. The method disclosedin this patent is relatively complex and determines the displacementbetween a plurality of well logs so they may be correlated and combined.The well logs are derived from multiple, spaced sensors passed one timethrough a single borehole, or from separate passes of the same sensorsthrough the same borehole. First, a normalized correlation functionbetween selected groups of samples of the sets of data is determined asa first assumption to have a predetermined displacement relationshipwith the groups of samples of the data. A step of determining thenormalized correlation function is repeated for a number of overlappinggroups of well log data samples to produce a number of overlappingcorrelation functions. At least some of these overlapping correlationfunctions are combined to produce an improved correlation function thatis used to depth correlate the well log data to a common, accurate depthlevel.

Another method for correlating well logging data collected by multiplesensors is taught in U.S. Pat. No. 6,272,232 issued Aug. 7, 2001 toJean-Pierre Delhomme and Jean F. Rivest. This patent teaches a methodfor constructing, from an initial image of the wall of a borehole, a new“crossing-component image” centered on the axis of the borehole. The newimage is representative of variations in a physical parameter of theearth formation in both the longitudinal direction of the borehole(depth), and in the peripheral direction of the borehole wall(laterally). The new image includes only those components of thephysical parameters that extend all the way across the initial boreholeimage from one side of the image to the other. The method also includesdetermining variations in one or more attributes relating to the newimage as a function of depth. The variations provide informationrelating to morphology to indicate solid zones, bedded zones, ordifferent types of heterogeneous zones.

When individual well logs are concurrently obtained from a first and asecond set of sensors vertically spaced from each other in a welllogging tool the well logs also need to be depth correlated. They needto be depth correlated so that the data for any given level in the welltaken by the two sets of vertically spaced sensors are aligned in orderto be useful. Another method for depth correlating well log data istaught in U.S. Pat. No. 4,320,469, issued Mar. 16, 1982 to William J.Frawley and Philip A. Mongelluzzo. This patent teaches doing this byusing data correlograms obtained by applying a correlation function to apair of digitized well logs to reduce the amount of data that must beprocessed. The remaining data is then processed in an efficient andaccurate manner in order to arrive at results indicating exactly howmuch two logs must be shifted with respect to each other for anoptimized depth correlation between them.

While methods for depth correlating data obtained using sensors spacedvertically from each other on a well logging tool, or obtained atseparate times of the same borehole are known, some of these methods arevery complex and there is a need for a better method to depth correlatedata obtained from well logging tool sensors.

DESCRIPTION OF THE DRAWINGS

The invention will be better understood upon reading the followingDetailed Description in conjunction with the drawings in which:

FIG. 1 shows a well logging tool in a borehole along with apparatus atthe surface of the earth for controlling the tool and recordingmeasurements derived therefrom;

FIG. 1A is a highly simplified representation of a portion of a welllogging tool showing the orientation of sensors thereon;

FIG. 2 is a picture of a portion of a well logging tool with its arms,pads and sensors;

FIG. 3A shows a bedding plane or fault intersecting a borehole at anangle relative to the axis of the borehole to create a dipping event andthe intersection is represented by an ellipse;

FIG. 3B shows a representation showing a portion of the wall of aborehole represented in FIG. 3A unrolled to a flat position;

FIG. 4 shows a display of signals obtained from sensors mounted on twosets of pads angularly distributed about the axis of a well loggingtool, with each set of pads being spaced vertically with relation toeach other;

FIG. 5 shows signals obtained from two sets of sensors spaced verticallywith relation to each other after depth correlating the signals forvertical offset;

FIG. 6 shows a block diagram of the steps involved to perform depthcorrelation by averaging individual sensor signals obtained at eachlevel of a well logging tool into a single signal, and the averagedsignals are then depth correlated to determine the optimum depth offsetnecessary for precisely matching signals;

FIG. 7 shows averaged two dimensional signals obtained from two sets ofsensors spaced vertically with relation to each other after beingtranslated into three dimensional Hough space to be used to determinedepth correlation to be applied to the signals; and

FIG. 8 shows a block diagram of the steps involved in translatingsignals taken from the two sets of sensors into three dimensional Houghspace to perform depth correlation.

DETAILED DESCRIPTION

The terms “depth match” and “depth matching” used hereinafter meancorrelating sets of data taken by different vertically spaced sensorsbelonging to different levels of sensors, such as sensors S1 a-S1 d andS2 a-S2 d in FIG. 1A, during a single pass of a logging tool through aborehole, or during different passes through a borehole. For ageological event, the vertical offset between different levels ofsensors causes signals coming from sensors in a first level of a loggingtool to be generated at a slightly different time than the signalscoming from sensors in a second level. The difference in these times isalso dependent on logging speed variations. The effects of thetime-offset need to be compensated to “depth match” the signals comingfrom the sensors at both levels.

Briefly, in a first embodiment of the present invention, individualtraces from the sensors of any first specific level of sensors on alogging tool are converted into one signal representing those traces.The one signal represents all the traces (averaged log signal) andincludes an average borehole-crossing signal. The averaged log signal isgenerated by performing a prior art computation of bedding dips orflowlines (angle and azimuth) on the traces from each sensor and anaverage or median computation is applied to all the samples fromsub-sensors that comprise each sensor aligned along the pre-determineddip. This is repeated for a second specific level of sensors verticallyoffset from the first specific level of sensors and a second averagedsignal is obtained. Then a prior art single log trace depth matchingtechnique is applied to two averaged signals to determine the optimumdepth “offset” necessary to precisely match the two averaged signals.The “offset” determined is then applied to the original traces from thesensors at one level to depth match them to the traces from the sensorsat the other level.

Briefly, in a second embodiment of the present invention the Houghtransform is utilized to generate three-dimensional images from well logsignals. The three dimensional images are used to create two-dimensionalextremum curves that are in turn used to calculate an offset. The offsetis used to depth match the well log signals obtained from verticallyspaced sensors on a well logging tool, or signals obtained duringdifferent logging passes through the same borehole. The detrimentaleffects of partial and non-overlapping sensor coverage of a boreholewall are reduced, if not eliminated, because of the characteristics ofthe Hough image transform, and because depth matching is finally appliedto the two dimensional extremum curves derived from thethree-dimensional images. More specifically, a depth matching offset iscalculated directly from two dimensional extremum curves derived fromthe Hough three-dimensional images without the need for calculating dipand azimuth of bed boundaries in an earth formation and compensating forit before the depth matching may be performed.

While the following description is given with reference to depthmatching data obtained from sensors on a borehole logging tool travelingthrough a borehole, the teaching of the present invention may beutilized with records, no matter how obtained or made. The records maybe a large number of azimuthally oriented traces obtained either fromsensors applied to a borehole wall, from sensors scanning a boreholeazimuthally, from sensors scanning azimuthally the cylindrical surfaceof a whole core, or from sensors probing an azimuthally oriented coresection cut, by stacking the pixels/measures along the apparent dipdirections seen on the core section cut.

In the following description only two sets of data are obtained from twosets of spaced sensors, and the data is correlated. This is done for thesake of clarity in describing the invention. However, the teaching ofthe invention may be used to correlate or depth match multiple sets ofdata. In addition, while the sets of data collected are described asbeing two-dimensional, some types of sensors may collectthree-dimensional data.

In the following description of a well logging system, prior artmaterial is not given in great detail to avoid detracting from anunderstanding of the two embodiments of the invention presented herein.For a more detailed understanding of any referenced prior art see theabove Background of the Invention and the references cited therein.

Referring to FIG. 1, there is shown an investigating tool 10 in aborehole 11 for investigating subsurface earth formations. Investigatingtool 10 is supported in borehole 11 on an end of a cable 12. Cable 12passes over a sheave wheel 13 and is secured to a drum and winchmechanism 14. The drum and winch mechanism 14 includes a suitable brushand slip ring arrangement for providing electrical connections betweenthe cable conductors and a control panel 15. The control panel 15operates to supply power and control signals to investigating tool 10,and includes suitable electronic circuitry for receiving well loggingsignals from sensors on the investigating tool. The well logging signalsmay be stored on a digital tape recorder 16.

Tape recorder 16 converts analog signals received from control panel 15into digital signals and is stepped as a function of depth by a drivingwheel 17 that engages cable 12. The digital signals are then eithertransmitted or carried to a computer system 18 for processing. Computersystem 18 comprises a processor, display and plotter for processing anddisplaying well logging data.

Investigating tool 10 has a reference point 20 that constitutes thecenter or recording point of tool 10. Because of long elastic cable 12,investigating tool 10 is subject to displacement arising from cablestretch thus causing the true depth level to be different from the depthlevel registered by a depth recorder 19 derived from driving wheel 17.The depth level registered by depth recorder 19, which is identical withthat registered by the tape recorder 16, is designated “Z”. Whenattempting to depth match well log data produced by different sensors ofinvestigating tool 10 there is a distinct possibility that the well logsrecorded at the same depth level will not be referenced to the samedepth level.

On investigating tool 10 sensors are located on two vertically spacedlevels L1 and L2 as shown, and their positions are described in greaterdetail starting in the next paragraph. These sensors produce the welllogging signals that are received by control panel 15.

FIG. 1A is a simplified representation of a portion of tool 10 aboutreference point 20 showing the layout of sensors thereon. Sensors areusually mounted on pads that engage the wall of a borehole or casing ina borehole, although the pads are not shown in FIG. 1A. In the highlysimplified arrangement described herein there is only one sensor on eachpad. In FIG. 1A the sensors are represented by boxes with an “x” thereinand are designated S1 a-S1 d in level L1 and S2 a-S2 d in level L2. InFIG. 2 there is shown a more detailed representation of an investigatingtool 10.

FIG. 1A shows two levels L1 and L2 of sensors positioned in two parallelplanes. Level L1 has four sensors S1 a-S1 d spaced ninety degrees apart,and level L2 has four sensors S2 a-S2 d spaced ninety degrees apart. Inone embodiment, the level L2 sensors are rotated or offset forty-fivedegrees with respect to the level L1 sensors. The spacing of the sensorsin each of levels L1 and L2, and the rotational offset between the twoplanes, results in the orientation of all the sensors around a boreholeas represented on the circle at the top of FIG. 1A.

An example of a sensor that may be used on tool 10 is one that measuresresistivity or conductivity to detect and measure boundary layers in aborehole. Such a sensor is taught in U.S. Pat. No. 4,786,874 issued Nov.22, 1988 to Donald S. Grosso and Allen Duckworth. The patented deviceutilizes electrical conductivity or resistivity to detect and measureboundary layers.

FIG. 2 is a picture of an actual well logging tool 10 with its arms 52a-52 d, pads 53 a-53 d, and sensors S1 a-S1 d thereon. Arms 52 a-52 dmove independently as tool 10 moves through a borehole to account forirregularities in the wall of the borehole. These arms also moveperpendicularly to the axis of a borehole to keep sensors on the pads incontact with the wall of the borehole. Pads 53 a-53 d are respectivelyconnected to arms 52 a-52 d and move therewith. On the surface of pads53 a-53 d are mounted sensors S1 a-S1 d. Each of the sensors S1 a-S1 dmay include a number of smaller sub-sensors.

When a bedding plane or fault intersects a borehole 11 at an anglerelative to the axis of the borehole, it is inclined or dipping andcreates a “dipping event” and the intersection is represented by anellipse 57 as shown in FIG. 3 a. In FIG. 3A are representatively shownfour traces 21 a-21 d taken by the four sensors S1 a-S1 d in level L1 ofFIG. 1A as the tool moves through the borehole. The traces are not shownextending longitudinally along the periphery of borehole 11 to avoidcluttering up FIG. 3A. The four traces intersect ellipse 57 at fourpoints Z₁-Z₄. These four points represent the different times at whichthe four sensors S1 a-S1 d will generate a signal representing the samedipping event as the sensors in level L1 are passed through borehole 11.

When the portion of the wall of borehole 11 represented in FIG. 3A isunrolled to a flat position, the ellipse 57 appears as a sinusoid 58 asshown in FIG. 3B. The location of trace-intersect points Z₁-Z₄ are shownon sinusoid 58. In addition, if traces 22 a-22 d in level L2 of FIG. 1Bwere shown plotted on FIG. 3A, which they are not since they are not inlevel L1, they would appear in FIG. 3B as the four intersect pointsZ₅-Z₈ and are interspaced between points Z₁-Z₄ on sinusoid 58 as shown.With all eight intersect points shown in FIG. 3B it can be seen how adipping event is represented as a sinusoid 58.

When the images of a dipping event are projected onto a flat surface, asshown in FIG. 3B, the vertical displacement of points Z_(i) (where i=1through 8) with respect to a point Z₀ will satisfy the mathematicalrelationship:δZ ₀ =r(φ,Z ₀ +δZ ₀)tan(α)sin(φ−β)where:

-   Z₀=depth of the center of the event along the longitudinal axis of    the borehole;-   φ=angle between north and the imaged point;-   δZ₀=Z=vertical distance between the center of the pattern at level    Z₀ and a point Z;-   α,β=dip and strike angle of the dipping event; and-   r(φ, Z₀+δZ₀)=radius of the borehole at point (φ,Z₀+δZ₀).

Thus, the vertical displacement distance δZ₀ from point Z₀ to each ofpoints Z₁-Z₄ in level L1 may be calculated.

r(φ, Z₀+δZ₀) for round cylindrical boreholes is constant and theborehole intersection is an ellipse. When the ellipse is unrolled, asdescribed above, the pattern seen is a sinusoid. The amplitude of thissinusoid is a function of the dip angle, and its phase is a function ofthe orientation of the surface with respect to north (strike angle orazimuth). For a non-cylindrical borehole, the intersection is not anellipse and the pattern is a distorted sinusoid. Obviously, the amountof distortion depends upon the degree of departure of the borehole froma perfect cylinder.

FIG. 4 shows displays 21 and 22 with traces 21 a-21 d and 22 a-22 drespectively. The set of traces 21 a-21 d is from the four sensors S1a-S1 d in level L1, and the set of traces 22 a-22 d is from sensors S2a-S2 d in level L2 as seen in FIG. 1A. The traces are obtained duringlogging of borehole 11. Each sensor may include at least one row ofsmaller sub-sensors. In addition, each sub-sensor generates a signal,and the side-by-side combination of such signals from the sub-sensorsgenerates the eight traces 21 a-21 d and 22 a-22 d.

It can be seen in display 21 that sensor S1 a produces trace 21 a at anarbitrarily assigned azimuth of 0 degrees. With the previously describedninety degrees spacing between sensors, sensor S1 b produces trace 21 bat an arbitrary azimuth of 90 degrees, sensor S1 c produces trace 21 cat an arbitrary azimuth of 180 degrees, and sensor S1 d produces trace21 d at an arbitrary azimuth of 270 degrees. The four level L2 sensorsS2 a-S2 d that produce traces 22 a-22 d have the same azimuthal spacingwith respect to one another as the level L1 sensors, i.e., the level L2sensors are spaced apart at ninety degrees among themselves. However, asshown in FIG. 1A, these sensors are oriented at a forty-five degreeoffset relative to the level L1 sensors as explained with reference toFIG. 1A. Accordingly, trace 22 a is at forty-five degrees, trace 22 b isat one-hundred thirty five degrees and so on.

As logging tool 10 moves along borehole 11, it may rotate horizontally asmall amount and its azimuth orientation may change. This creates thehorizontal image skewing of the four traces shown in each of displays 21and 22. The skewing is shown as the traces not being in a vertical,straight line.

Superimposed on display 21 are drawn two sinusoidal waveforms 26 and 27that reflect common borehole crossing features shown in traces 21 a-21d. “Borehole crossing features” designate rock features that are goingacross the borehole as opposed to smaller localized rock features thatmay be seen by fewer than all the pads of a level of sensors. Similarly,superimposed on display 22 are two sinusoidal waveforms 28 and 29 thatreflect common borehole crossing features shown in traces 22 a-22 d.

As is known in the prior art, and as previously described with referenceto FIGS. 3A and 3B, sinusoidal waveforms 26-29 always reflect a “dip” ina bedding plane or fault that intersects borehole 11. The amplitude ofthe waveforms indicates the degree or angle of dip, and the location ofthe peaks of the waveforms (phase) indicates the direction or azimuth ofthe dip.

As traces 21 a-21 d and 22 a-22 d of displays 21 and 22 are generatedfrom sensor signals taken in the same borehole, they generally wouldlook alike except for a vertical displacement 30, reflecting the spacingbetween the level L1 and L2 sensors, and the azimuth offset between thelevel L1 and L2 sensors. The vertical displacement of the traces inimages 21 and 22 reflects the fact that sensors S1 a-S1 d are physicallylocated above sensors S2 a-S2 d on logging tool 10 as shown on FIG. 1A.In addition, some vertical displacement may be caused by other factorssuch as stretching of cable 12 as previously described.

FIG. 4 also shows single borehole crossing traces 23 and 24 that areobtained from the individual traces 21 a-d and 22 a-d shown in thisFigure. Each single trace 23 and 24 respectively represents one set oftraces 21 a-21 d and 22 a-22 d, each set being converted into singletraces 23 and 24 respectively. In the first embodiment of the invention,traces 23 and 24 are obtained by performing an average or medianoperation among each corresponding set of traces 21 a-21 d and 22 a-22d, each trace 23 and 24 representing the average value of a specificearth (rock) feature crossing the borehole.

Each of the average traces 23 and 24 is generated by first performing aprior art computation of bedding dips or flowlines on the individualtraces from each sensor of a specific level. As a result, sinusoidalwaveforms, such as 26 are obtained. Then, an average or mediancomputation is applied to all the sample images (responses fromsub-sensors) located along the sinusoid waveform 26 (bedding dip)obtained. By averaging the signals along bedding dips, the common partof the signals that is due to bedding is enhanced and the localized partthat is due to heterogeneities, such as gravel, vugs, etc., isattenuated. This is desirable as the common part may be expected to befound on all levels of sensors and thus be useable for depth matchingcorrelation.

The determination of a sinusoidal waveform relies on the dip and azimuthof each bed boundary. The dip and azimuth of a bed boundary as afunction of depth in a borehole may be determined from traces of theborehole by using prior art techniques such as the Hough transformdescribed in the background of the invention.

As signals 23 and 24 are obtained, a single log trace depth matchingtechnique is applied to these signals to determine an optimum depth“offset” for depth matching signal 24 to signal 23. The “offset”determined is then applied to traces 22 a-22 d to depth match them totraces 21 a-21 d as seen in FIG. 5.

The averaged traces 23 and 24 may be determined mathematically asfollows. First, the intersection between a bedding plane and theborehole at a given depth Z₀ may be expressed mathematically as follows.Z=Z ₀ +A(Z ₀)cos(φ−φ₀(Z ₀))where the Greek symbols φ and Z are the coordinate system of theborehole image space, and A(Z₀) and φ₀(Z₀) are the amplitude and azimuthof the bedding plane at the depth Z₀.

The average signal trace at depth Z₀, S(Z₀), is then calculated asfollows. Let I(φ, Z) be the pixel values of the traces comprising aborehole image.

for each depth Z₀: S(Z₀)=Σ_(φ)(I (φ, Z₀+A(Z₀)cos(φ−φ₀(Z₀))/N_(V); withN_(V) being the number of valid pixels (non-absent) along a sinusoid atdepth Z₀.

Depth values Z₀ may be obtained by way of the teaching set forth in thereferences cited in the background of the invention (apparatus andmethods for determining the required accurate depth measurements). Theprior art teaches using such things as cables on a precision winch, adepth wheel measurement instrument, and sometimes an axial accelerometerwhose output is integrated to help overcome the known problems inherentin precisely measuring how deep a well logging tool is in a borehole.These depth measurements are shown as the 100 depth unit and 110 depthunit measurements on the graphs in FIGS. 4 and 5.

After the averaged signals S(Z₀) are calculated, and displayed as traces23 and 24, the teaching of the prior art is used to correlate theaveraged waveforms 23 and 24 to determine a depth offset 30 betweenthem. One prior art technique for obtaining a measure of correlation todepth match two logs is disclosed in the U.S. Pat. No. 4,312,040, issuedJan. 19, 1982 to David H. Tinch, Bruce N. Carpenter and Elie S. Eliahou.The technique taught in this patent involves comparing two depth shiftedwell logs, and determining a correlation function indicating how closelythe two logs match each other at a plurality of depth levels.

The depth correlation teaching of the Tinch et al patent is succinctlysummarized at col. 10, 1.56 through col. 11, 1.32. Specific detail ofthe correlation process taught in this patent is given at col. 8, 1.16through col. 10, 1.39.

Briefly, referring to the summarization starting at col. 10, 1.56 in theTinch et al patent, two well logs A and B, such as from levels L1 andL2, to be correlated are initially considered to be depth matched inaccordance with the depth indicia on magnetic tape on which the log datais recorded, such as the depth from depth recorder 19 on recorder 16 inFIG. 1. Beginning at an initial depth level Z_(a) in a borehole, a firstassumed value of the depth displacement is computed between the B logand the A log at each selected depth level from Z_(a) to Z_(b) inincrements of Δ_(y). The A log is considered to be the base log and thedisplacement for the B log relative to the A log is computed.

Concerning the depth correlation process at one depth level, the B logis effectively shifted one step Δ_(z) at a time and a correlationfunction C_(K) is computed at each such step using equation (1) shown incol. 4 of the Tinch et al patent. Once the correlation values of C_(K)over the entire search interval 2ΔZ_(C) are computed, the value of Kwhich produced the maximum value of C_(K), designated K′, is determined.The corresponding depth displacement will be (K′−K_(max/2)ΔZ_(o). Thus,for example, if ΔZ_(o) is 1 inch and (K′−K_(max/2)) is −6, the computeddepth displacement for log B at the presently considered depth level Zwill be −6 inches. However, this depth displacement is not computedunless C_(K)(max) is equal to or greater than C_(K)(lim). This preventsweak correlation quantities from causing depth displacements. IfC_(K)(max) is greater than C_(K)(lim), the displacement SH(Z) iscomputed and entered into the history file for statistical analysis.This computed value SH(Z) is only a first assumption of the depthdisplacement which may be changed by the statistical analysis.

This statistical analysis takes the form of declaring a depthdisplacement only when a consecutive number of identical depthdisplacements have been computed. By so doing, an occasional erroneousdepth displacement caused by noise, for example, will not cause log B tobe depth displaced.

After a depth matching offset has been calculated for waveforms 23 and24, according to the method of the above cited Tinch et al patent, thecalculated offset is applied to traces 22 a-22 d shifting (depthtranslating) them upward as seen in FIG. 5. The shift is seen whencomparing these traces in FIG. 5 with the same traces in FIG. 4. Traces21 a-21 d are thus depth matched to traces 22 a-22 d.

When there are more than two sets of data to be depth matched theprocess is basically the same as described above for two sets of data.The difference is that one set of data (from the sensors at one depth)is used as a reference set of data and the offset therefrom to each ofthe other data sets is determined. The offset calculated for each of theother data sets is then applied to the other data sets to depth match tothe reference data set.

In FIG. 6 is shown a block diagram of the steps involved in performingdepth correlation of different sets of signal traces in accordance withthe teaching of the first embodiment of the invention. At block 31borehole images represented by the traces 21 a-21 d from sensors S1 a-S1d are obtained and oriented azimuthally. At block 32 borehole imagesrepresented by the traces 22 a-22 d from sensors S2 a-S2 d are obtainedand oriented azimuthally.

As previously described, the two sets of traces 21 a-21 d and 22 a-22 dreflect dip of bedding layers in the borehole and also reflect theazimuths of the dips. At block 35 the dip indicated by each of thesesets of images is calculated using a prior art dip calculation techniquesuch as the one applying the Hough transform described in the patentmentioned in the background of the invention in connection with theHough transform.

At block 36 the calculated dip for traces 21 a-21 d is used along withthe traces themselves to generate a single trace 23. Similarly, thecalculated dip for the traces 22 a-22 d is used along with the tracesthemselves to generate a single trace 24.

At block 37 a prior art single log trace depth matching technique, suchas taught in the above cited and described Tinch et al patent, isapplied to traces 23 and 24 to determine the optimum depth offsetnecessary for precisely matching the borehole traces 22 a-22 d to traces21 a-21 d. At block 38 the traces 22 a-22 d are shifted relative totraces 21 a-21 d to depth match them.

In a second embodiment of the present invention, two-dimensional welllog traces 21 a-21 d and 22 a-22 d of FIG. 4 are transformed into threedimensional Hough space using the Hough transform to get threedimensional images of which only one representative slice 39 and 40 areshown in FIG. 7. The Hough transform is well known and used in the priorart to transform two-dimensional well logs into three-dimensional Houghspace images from which dip and azimuth is determined. The Houghtransform as used herein transforms a sinusoidal waveform into a pointin a three dimensional space and a plurality of sinusoidal waveformsmaking up the two-dimensional space into the three dimensional Houghspace images. These images are made up of a plurality of image slices 39and 40. Slice 39 is one of the slices of the three-dimensional imageproduced by the Hough transform from well log traces 21 a-21 d. Slice 40is one of the slices of the three-dimensional image produced by theHough transform from well log traces 22 a-22 d.

Depth matching is accurately and automatically accomplished using thethree-dimensional images created by the Hough transform from welllogging traces 21 a-21 d and 22 a-22 d. The three-dimensional Houghimages have properties that make them suitable for depth matching ofwell logging images. Those properties are: (1) insensitivity to gaps(missing data) in the original well logging images (the gaps in theoriginal well logging images are the spaces between traces 21 a-21 d andbetween 22 a-22 d in FIGS. 4 and 5), (2) insensitivity to rotation andorientation of the pads, and (3) dip in the well logging images does nothave to be calculated before depth matching of the well logging imagesis performed.

Then, according to the second embodiment of the present invention,extremum curves 42 and 43, representing traces 21 a-21 d and 22 a-22 drespectively, are produced from the three-dimensional Hough images. Theextremum curves 42 and 43, reflect certain rock features in the earth,and represent peak values in the three dimensional space at a givendepth. The image signal peaks (local maxima) in the three dimensionalHough images 39 and 40 appear as peaks in the extremum curves 42 and 43.

Automatic depth matching is performed directly on extremum curves 42 and43 without the need for calculating dip and azimuth of bed boundaries inan earth formation and compensating for it before depth matching may beperformed, as in the prior art. A prior art depth matching algorithm isthen applied to the two-dimensional extremum curves 42 and 43 derivedfrom the Hough image slices, such as 39 and 40, to thereby determine adepth shift offset that will correlate extremum curves 42 and 43. Thedepth shift offset that is determined is thereafter applied to traces 22a-22 d to depth match them to traces 21 a-21 d as seen in FIG. 5.

Prior art examples of depth matching algorithms that can be used tocorrelate the extremum curves may be the same as those utilized by thefirst embodiment and may be found in: (1) U.S. Pat. No. 4,320,469,issued Mar. 12, 1982 to William J. Frawley, and Philip A. Mongelluzzo,and (2) U.S. Pat. No. 4,312,040, issued Jan. 19, 1982 to David H. Tinch,Bruce N. Carpenter and Elie S. Eliahou.

The Hough transform utilized in the second embodiment of the inventionis described in two papers: (1) J. Illingworth and J. Kittler, “A Surveyof the Hough Transform”, Computer Vision, Graphics, Image Processing 44(1988), p. 87-116; and (2) V. F. Leavers, “Which Hough Transform?”,CVGIP: Image Understanding 58 (1993), No. 2, p. 250-264. See also U.S.Pat. No. 5,960,371 issued Sep. 28, 1999 to Naoki Saito, Nicholas N.Bennett and Robert Burridge cited in the background of the invention;and a paper by J. Illingworth and J. Kittler, “A Survey of the HoughTransform” Computer Vision, Graphics and Image Processing, vol. 44,(1988) pp. 87-116.

How the Hough Transform can transform images from a defined coordinatesystem to a different coordinate system is more fully explained in anarticle entitled “Use of the Hough Transform to Detect Lines and Curvesin Pictures”, Duda, R. P. and Hart, P. E., ACM, vol. 15, no. 1 pp.11-15. The Hough transform technique was initially developed to detectstraight lines in binary images. However, due to its simplicity, thetechnique was extended to detect other types of simple analytic shapeslike circles and ellipses and is used today to recognize patterns evenwhen they do not have an analytic description.

The use of the Hough transform to automatically extract features orgeometric parameters from borehole images was first taught in U.S. Pat.No. 3,069,654 issued Dec. 18, 1962 to P.V.C. Hough. By using the Houghtransform to analyze “dip” events they appear as image signal peaks inHough three-dimensional space. The use of the Hough transform to measuredip and azimuth of geological beds is also taught in U.S. Pat. No.5,162,994, issued Nov. 10, 1992 to David O. Torres.

The Hough transform makes it possible to determine, from an image, thespecific parameters characterizing a geometrical shape such as astraight line, a circle, an ellipse, or a sinusoid curve, such as curves26-29 in FIG. 4. The Hough transform then projects points of theseshapes into three dimensional parameter space referred to as Houghspace. More specifically, when the Hough Transform is used to processdata points on a two-dimensional line or curve they are, mathematicallyspeaking, transformed into three dimensional parameter space where thedip and strike angles are dimensions within the parameter space.

Generally, according to Hough formalism every sinusoid is atwo-dimensional curve that may be mathematically expressed as follows.An abscissa φ, and an ordinate Z where Z can be expressed as: Z=Z₀+Acos(φ−φ₀). When mathematically developing this equation for the Houghtransform we get: Z=Z₀+A cos φ₀cos φ+A sin φ₀sin φ. We then set X₀=+Acos φ₀ and Y₀=+A sin φ₀ and the equation becomes Z=Z₀+X₀cos φ+Y₀ sin φ.In these equations A is the amplitude of a dip indicated by the twodimensional sinusoid in a well log image, φ₀ is the offset (phase) ofazimuth of the dip, and Z₀ is the zero crossing depth of the sinusoid.The Greek symbols φ and Z are the coordinate system of the logging imagespace, and X₀, Y₀ and Z₀ are the coordinate system of the threedimensional Hough image space.

For example, by performing a summation along the sinusoidal waveform ofthe logging image pixel measurements, a value may be obtained andassociated to a point (X₀, Y₀, Z₀) in the Hough space. The valueobtained is high if the sinusoid associated to a point in the Houghspace lies on a sinusoidal feature having a high pixel value in a welllogging image. Conversely, the obtained value is low if the sinusoidassociated with a point lies on a sinusoidal feature having a low pixelvalue in a well logging image. In the case where there is no clearsinusoidal feature in the well logging image, a medium backgroundmeasurement is obtained.

The following algorithm is then used to generate extermum curves fromthree dimensional Hough images in order to apply a prior art depthmatching algorithm:

Let H(X₀, Y₀, Z₀) be a 3D array of the Hough transform.

-   -   1. Compute H_(average), the mean value of H(X₀, Y₀, Z₀) one time        for the whole array    -   2. Centralize H(X₀, Y₀, Z₀) in the value domain:        -   H_(c)(X₀, Y₀, Z₀)=H(X₀, Y₀, Z₀)−H_(average)    -   3. For each depth Z₀, find the maximum absolute value V(Z₀) of        H_(c):        -   V(Z₀)=max_(X0.Y0){abs(H_(C)(X₀, Y₀, Z₀)) at Z₀}

From the property of the Hough transform described above one can seethat, at each depth Z₀, where the curve V(Z₀) is at a local maximum,there must be a dip event (either peak or trough) in the form of asinusoid, such as sinusoids 26-29 in FIG. 4. Thus, the extremum curveV(Z₀) characterizes the logging image and is a good candidate forapplying a depth matching algorithm.

In FIG. 8 is shown a block diagram of the steps involved in translatingsignals taken from the two sets of sensors S1 a-S1 d and S2 a-S2 d intothree dimensional Hough space (FIG. 7) to determine a depth matchingoffset to be used to match traces 21 a-22 d and 22 a-22 d in accordancewith the teaching of the second embodiment of the invention. At block 44traces 21 a-21 d in level L1 are obtained, and at block 45 traces 22a-22 d in level L2 are obtained, both using prior art apparatus andtechniques as described in the background of the invention.

At block 46 traces 21 a-21 d in Level L1 are processed using the Houghtransform to produce the three-dimensional Hough image of which oneslice is shown as image 39 in FIG. 7. Also, at block 47 traces 22 a-22 din Level L2 are processed using the Hough transform to produce thethree-dimensional Hough image of which one slice is shown as image 40 inFIG. 7.

At block 48 the three-dimensional Hough image produced in block 46 isused to compute a two-dimensional extremum curve, and at block 49 thethree-dimensional Hough image produced in block 49 is used to compute atwo-dimensional extremum curve.

At block 50 a depth shift offset is calculated using the two extremumcurves. As previously described, extremum curves 42 and 43 are createdfrom the three-dimensional Hough images 39 and 40. An automatic depthmatching calculation is performed directly on the extremum curves,without the need for calculating dip and azimuth of bed boundaries in anearth formation, to calculate a depth match offset.

At block 51 the calculated depth match offset calculated from theextremum curves is then used to depth match traces 21 a-21 d and 22 a-22d as shown in FIG. 5. Being as signal traces 21 a-21 d and signalstraces 22 a-22 d are offset by forty-five degrees as previouslydescribed, the overlaid, depth matched traces now show combined dataevery forty-five degrees around the borehole as represented in FIG. 1A.

When there are more than two sets of data to be depth matched theprocess is basically the same as described for two sets of data. Thedifference is that one set of data (from the sensors at one depth) isused as a reference set of data and. The vertical offset therefrom toeach of the other plurality of data sets is determined and then appliedto the other data sets to depth match to the reference data set. Asapplied to the use of the Hough transform, a plurality oftwo-dimensional well log traces are each transformed intothree-dimensional Hough space using the Hough transform to get threedimensional images. Extremum curves are then derived from each of thethree-dimensional Hough images. Automatic depth matching is thenperformed directly on the extremum curves, as previously described.Using the extremum curves resulting from one set of data as a reference,a prior art depth matching algorithm is then used to compare theextremum curves representing the reference data set with the extremumcurves representing each of the plurality of other data sets to therebydetermine a depth shift offset that will correlate them to the referenceset. The depth shift offset that is determined using each set ofextremum curves is then applied to the corresponding data set to depthmatch it to the reference data set.

The above description describes two embodiments of a system whereinborehole logging data is collected by sensors on a logging tool passingthrough a borehole. The sensor signals representing the data aretransmitted via a cable to the earth surface, as shown in FIG. 1, to bestored and processed. However, in an alternative embodiment of theinvention, computer processor and storage capability may be added to thelogging tool and depth match processing of the data from the sensors isdone in real time in-situ. The depth matched data is then eitherextracted from storage after the logging tool is extracted from theborehole, or the real time depth matched data is transmitted to thesurface of the earth over cables that transmit data from sensors toabove ground equipment as shown in FIG. 1. Alternatively, the depthmatched data from the processor at the logging tool may be transferredfrom the logging tool to the surface using remote telemetry capability.A transmitter with the logging tool transmits the depth matched datadetermined by the receiver downhole to a receiver on the surface of theearth without the need for a physical connection between the downholelogging tool and the receiver. Once the depth matched data is receivedby the receiver it may be transmitted to a location from the boreholefor analysis or other processing.

What has been described above also applies to images of borehole wallsand borehole core, irrespective of the measured parameter which formsthe images such as, for example, rock conductivity, resistivity,magnetic susceptibility, photoelectric factor, density of the formation,amplitude of acoustic reflections, photographic brightness, etc. Inaddition, an image from one logging run in a borehole may be compared toan image from another logging run in the same borehole, and an imagefrom a borehole may be compared to an image of a core from the borehole.In addition, images obtained from a cased borehole may be depth matchedusing the teaching of the present invention. Further, the presentinvention may be used to depth match logs obtained by a logging toolfrom a borehole during coring as taught in U.S. Pat. No. 6,003,620issued Dec. 21, 1999 to Mukul M. Sharma, Roger T. Bonnecaze and BernardZemel.

For the sake of simplicity only, a simple arrangement for a logging toolis described. There are pads and sensors on two levels, each levelhaving four pads spaced ninety degrees apart, and there being one sensoron each pad. The pads in one level are rotated forty five degrees withrespect to the pads in the other level. There may be more than four padsin each level; the pads may be spaced other than equiangularly; the padsin one level may be rotated at angles other than forty-five degrees withrespect to the pads in the other level; and there may be many moretransducers on each pad. In addition, data or images from any type oftransducer, sensor, scanner or camera may be processed and depth matchedusing the teaching of the present invention in both of its embodiments.

1. A method for matching a plurality of data sets from boreholes or coresections, the data sets being obtained from sensors are two-dimensionaldata sets and are indicative of earth formation, boundary, or interfaceof earth formations and of dip in the vicinity of the borehole, themethod for depth matching comprising: (a) the two-dimensional data setsare transformed into three-dimensional images using the Hough transform;(b) two dimensional curves are derived from the three-dimensional imagesby the application of the Hough transform to depth derivatives of sensorsignals, generated by sensors; and (c) an offset is derived from thetwo-dimensional curves for applying to the two dimensional data sets todepth match them to each other.
 2. The method in accordance with claim 1wherein the two dimensional curves have peaks indicating dip events inthe vicinity of the borehole.
 3. The method in accordance with claim 1wherein the two-dimensional data sets have gaps in the data and thethree-dimensional images created using the-Hough transform are immunefrom the gaps.
 4. The method in accordance with claim 1 whereintwo-dimensional curves for data sets from sensors that are verticallyspaced from each other longitudinally along the borehole are processedto determine an offset that will match the two-dimensional curves. 5.The method in accordance with claim 4 wherein the determined offset isapplied to the data sets from the vertically spaced sensors to depthmatch the data sets to each other.
 6. A method for matching a pluralityof data sets from boreholes or core sections, the data sets beingobtained from sensors are two-dimensional data sets and are indicativeof a boundary, or interface of earth formations and of dip in thevicinity of the borehole, the method for depth matching comprising: foreach two-dimensional data set of the plurality of data sets, individualsignals making up the respective two-dimensional data set are combinedto create an averaged signal; averaged signals, each corresponding toone two-dimensional data set, are processed to calculate an offset thatcorrelates the averaged signals; and the calculated offset is applied tothe two-dimensional data sets to depth match them to each other.
 7. Themethod of claim 6 wherein said averaged signals are obtained bydetermining an average of the sensor signals along the bedding dip for agiven depth in the borehole.
 8. The method of claim 7 wherein saidcomputation of bedding dips for the sensor signals is performed by wayof the Hough transform.
 9. The method in accordance with claim 1 whereintwo-dimensional data sets to be depth matched are obtained at the sametime by sensors that are vertically spaced from each otherlongitudinally along the borehole.
 10. The method in accordance withclaim 1 wherein two-dimensional data sets to be depth matched areobtained at different times for the same borehole.
 11. The method inaccordance with claim 1 wherein a two-dimensional data set to be depthmatched is obtained from a core section.
 12. The method of claim 1wherein each of said sensor signals is obtained from a sensor of aplurality of sensors.
 13. The method of claim 12 wherein each sensorincludes a plurality of sub sensors.
 14. The method of claim 13 whereineach signal includes a trace, the trace being a side-by-side combinationof signals from the plurality of sub sensors.
 15. The method inaccordance with claim 1 wherein said method is applicable to real timedepth matching of data sets from sensors that are vertically spaced fromeach other longitudinally along the borehole.
 16. The method inaccordance with claim 6 wherein two-dimensional data sets to be depthmatched are obtained at the same time by sensors that are verticallyspaced from each other longitudinally along the borehole.
 17. The methodin accordance with claim 6 wherein two-dimensional data sets to be depthmatched are obtained at different times for the same borehole.
 18. Themethod in accordance with claim 6 wherein a two-dimensional data set tobe depth matched is obtained from a core section.
 19. The method ofclaim 6 wherein each of said sensor signals is obtained from a sensor ofa plurality of sensors.